The dependence of spectral impedance on disc microelectrode radius

As microelectrodes gain widespread use for electrochemical sensing, biopotential recording, and neural stimulation, it becomes important to understand the dependence of electrochemical impedance on microelectrode size. It has been shown mathematically that a disc electrode, coplanar in an insulating substrate and exposed to a conducting media, exhibits an inhomogeneous current distribution when a potential step is applied. This distribution is known as the primary distribution, and its derivation also yielded an analytic solution for electrical resistance of the conducting media (R(s)), between the disc surface and a distant ground, which is inversely proportional to disk radius [R(s) = 1/(4kappar), where kappa is media conductivity and r is disk radius]. The dependence of spectral impedance on microelectrode radius, however, has not been explored. We verify the analytical solution for resistance using high-frequency (100 kHz) electrochemical impedance data from microelectrodes of varying radius (11-325 microm). For all disc radii, as we approach a lower frequency (--> 10 Hz), we observe a transition from radial to area dependence (e.g., 1/r --> 1/r2). We hypothesize that this transition is driven by the fact that the derivation of the primary distribution ignores concentration gradients, but that these gradients cannot be ignored at lower frequencies.